From the Code of Canon Law:
Can. 1086 §1. A marriage between two persons, one of whom has been baptized in the Catholic Church or received into it -]and has not defected from it by a formal act/-] * and the other of whom is not baptized, is invalid.
§2. A person is not to be dispensed from this impediment unless the conditions mentioned in cann. 1125 and 1126 have been fulfilled.
§3. If at the time the marriage was contracted one party was commonly held to have been baptized or the baptism was doubtful, the validity of the marriage must be presumed according to the norm of can. 1060 until it is proven with certainty that one party was baptized but the other was not.
Can. 1125 The local ordinary can grant a permission of this kind if there is a just and reasonable cause. He is not to grant it unless the following conditions have been fulfilled:
1/ the Catholic party is to declare that he or she is prepared to remove dangers of defecting from the faith and is to make a sincere promise to do all in his or her power so that all offspring are baptized and brought up in the Catholic Church;
2/ the other party is to be informed at an appropriate time about the promises which the Catholic party is to make, in such a way that it is certain that he or she is truly aware of the promise and obligation of the Catholic party;
3/ both parties are to be instructed about the purposes and essential properties of marriage which neither of the contracting parties is to exclude.
Can. 1126 It is for the conference of bishops to establish the method in which these declarations and promises, which are always required, must be made and to define the manner in which they are to be established in the external forum and the non-Catholic party informed about them.
Can. 1127 §1. The prescripts of can. 1108 are to be observed for the form to be used in a mixed marriage.
Nevertheless, if a Catholic party contracts marriage with a non-Catholic party of an Eastern rite, the canonical form of the celebration must be observed for liceity only; for validity, however, the presence of a sacred minister is required and the other requirements of law are to be observed.
§2. If grave difficulties hinder the observance of canonical form, the local ordinary of the Catholic party has the right of dispensing from the form in individual cases, after having consulted the ordinary of the place in which the marriage is celebrated and with some public form of celebration for validity. It is for the conference of bishops to establish norms by which the aforementioned dispensation is to be granted in a uniform manner.
§3. It is forbidden to have another religious celebration of the same marriage to give or renew matrimonial consent before or after the canonical celebration according to the norm of §1. Likewise, there is not to be a religious celebration in which the Catholic who is assisting and a non-Catholic minister together, using their own rites, ask for the consent of the parties.
Can. 1128 Local ordinaries and other pastors of souls are to take care that the Catholic spouse and the children born of a mixed marriage do not lack the spiritual help to fulfill their obligations and are to help spouses foster the unity of conjugal and family life.
Can. 1129 The prescripts of cann. 1127 and 1128 must be applied also to marriages which the impediment of disparity of cult mentioned in can. 1086, §1 impedes.
*This line was removed from Canon Law with the promulgation of Pope Benedict's motu proprio Omnium In Mentem on October 26, 2009.